This came partially out of the fact that Roman women were not so economically dependent. They could inherit in their own names and own property in their own right. After the passing of the Julian Marriage Laws, a widow with three or four children was free from guardianship. Even a widow still under guardianship had a certain amount of freedom, especially if she had property. It is worth noting, however, that a widow could still be accused of adultery.*
Unsurprisingly, there was a certain amount of tension between the ideal of the married state presented by the Julian Marriage Laws and the ideal of the univira. As part of an attempt to increase the birthrate, the Laws rewarded remarriage after divorce or widowhood and discouraged both men and women from remaining single. The ideal of the univira, however, remained strong. To remain single was the social ideal. To remarry was the course encouraged by the law. The two ideas remained in tension for the next several hundred years.
*By the 2nd century at least, a father of a married woman had preference in accusing (and attacking) his daughter if he caught her in the act of adultery (but only if he caught her in the act). The father of a widow had no such preference.
**I have seen it argued that Tiberius prevented Agrippina from remarrying despite her own desires. Most scholars, however, agree that it was her own decision.
Papinian, On Adultery, book 2 (Digest 48.5.11) - Diotima
Papinian, On Adultery, book 1 (Digest 48.5.23) - Diotima
Plutarch, Life of Tiberius Gracchus, 1.2-2 G - Diotima
Olasope, Olankunbi O. "Univira: the Ideal Roman Matrona." Lumina 20.2 (2010): 1-18. Can be found here.
Roman Weddings - Classics Technology Center
Hanson, Ann. "Women and Family Archives on Papyrus" - Diotima